Typically we use an ellipsis (...) to show that a number continues on; e.g.:
1/3 = 0.33333...Even in the English language, it is used to indicate that something continues on and on, like so:
The team just kept scoring goal after goal after goal...
But what if a number continues irrationally? My favorite constant, e, is often written like so:
e: 2.718281...Even in wikipedia, continuation of our beloved Pi is shown to continue on with an elipsis
Pi: 3.1415927...Wouldn't it make sense to use a different symbol? Say, a tilde:
Pi: 3.1415927~Is there a symbol in existence to indicate that a number continues irrationally?
$\endgroup$ 31 Answer
$\begingroup$I think the ellipsis is the symbol for "continues irrationally", or at least for "continues, not necessarily rationally".
If you wish to indicate that a decimal "continues rationally", you do so with an overbar:
$$\dfrac 1 3 = 0.\overline{3}$$
$$\dfrac{4}{33}=0.\overline{12}$$
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